Öz
In this paper, we study skew cyclic codes over the ring $R=\mathbb{F}_{q}+u\mathbb{F}_{q}+v\mathbb{F}_{q}+uv\mathbb{F}_{q}$, where $u^{2}=u,v^{2}=v,uv=vu$, $q=p^{m}$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $R$ through a decomposition theorem. Furthermore, we give a formula for the number of skew cyclic codes of length $n$ over $R.$
Anahtar Kelimeler
Linear codes Skew cyclic codes Gray map Generator polynomial
Kaynakça
- T. Abualrub and P. Seneviratne, Skew codes over rings, in Proc. IMECS, Hong Kong, II, 2010.
- F. W. Anderson and K. R. Fuller, Rings and categories of modules, Springer, 1992.
- D. Boucher, W. Geiselmann and F. Ulmer, Skew cyclic codes, Appl. Algebra Engrg. Comm. Comput., 18(4), 379-389, 2007.
- D. Boucher and F. Ulmer, Coding with skew polynomial ring, J. Symb. Comput., 44(12), 1644-1656, 200
- D. Boucher, P. Sol´e and F. Ulmer, Skew constacyclic codes over Galois ring, Adv. Math. Commun., 2(3), 273-292, 2008.
- J. Gao, Skew cyclic codes over Fp+ vFp, J. Appl. Math. Inform., 31(3,4), 337-342, 2013.
- J. Gao, L. Z. Shen and F. W. Fu, Skew generalized quasi-cyclic codes over finite fields, arXiv preprint arXiv:1309.1621, 2013.
- F. Gursoy, I. Siap and B. Yildiz, Construction of skew cyclic codes over Fq+ vFq, Adv. Math. Commun., 8(3), 313-322, 2014.
- F. Hernando and D. Ruano, Sixteen new linear codes with Plotkin sum, arXiv preprint arXiv:0804.3507, 2008.
- S. Jitman, S. Ling and P. Udomkavanich, Skew constacyclic over finite chain rings, Adv. Math. Commun., 6(1), 29-63, 2012.
- A. R. Hammons Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Solé, The Z-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inform. Theory, 40(2), 301-319, 1994.
- I. Siap, T. Abualrub, N. Aydin and P. Seneviratne, Skew cyclic codes of arbitrary length, Int. Nat. Sci., 2(1), 10-20, 2011.
- Y. T. Zhang, Research on constacyclic codes over some classes of finite non-chain rings, Master’s thesis, Hefei University of Technology, 2013.
Öz
Kaynakça
- T. Abualrub and P. Seneviratne, Skew codes over rings, in Proc. IMECS, Hong Kong, II, 2010.
- F. W. Anderson and K. R. Fuller, Rings and categories of modules, Springer, 1992.
- D. Boucher, W. Geiselmann and F. Ulmer, Skew cyclic codes, Appl. Algebra Engrg. Comm. Comput., 18(4), 379-389, 2007.
- D. Boucher and F. Ulmer, Coding with skew polynomial ring, J. Symb. Comput., 44(12), 1644-1656, 200
- D. Boucher, P. Sol´e and F. Ulmer, Skew constacyclic codes over Galois ring, Adv. Math. Commun., 2(3), 273-292, 2008.
- J. Gao, Skew cyclic codes over Fp+ vFp, J. Appl. Math. Inform., 31(3,4), 337-342, 2013.
- J. Gao, L. Z. Shen and F. W. Fu, Skew generalized quasi-cyclic codes over finite fields, arXiv preprint arXiv:1309.1621, 2013.
- F. Gursoy, I. Siap and B. Yildiz, Construction of skew cyclic codes over Fq+ vFq, Adv. Math. Commun., 8(3), 313-322, 2014.
- F. Hernando and D. Ruano, Sixteen new linear codes with Plotkin sum, arXiv preprint arXiv:0804.3507, 2008.
- S. Jitman, S. Ling and P. Udomkavanich, Skew constacyclic over finite chain rings, Adv. Math. Commun., 6(1), 29-63, 2012.
- A. R. Hammons Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Solé, The Z-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inform. Theory, 40(2), 301-319, 1994.
- I. Siap, T. Abualrub, N. Aydin and P. Seneviratne, Skew cyclic codes of arbitrary length, Int. Nat. Sci., 2(1), 10-20, 2011.
- Y. T. Zhang, Research on constacyclic codes over some classes of finite non-chain rings, Master’s thesis, Hefei University of Technology, 2013.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 14 Eylül 2015 |
| Yayımlandığı Sayı | Yıl 2015 Cilt: 2 Sayı: 3 |